9x(4x-6)=17+2(3x+8)

Solution for 9x(4x-6)=17+2(3x+8) equation:

9x(4x-6)=17+2(3x+8)

We move all terms to the left:

9x(4x-6)-(17+2(3x+8))=0

We multiply parentheses

36x^2-54x-(17+2(3x+8))=0


We calculate terms in parentheses: -(17+2(3x+8)), so:

17+2(3x+8)

determiningTheFunctionDomain
2(3x+8)+17

We multiply parentheses

6x+16+17

We add all the numbers together, and all the variables

6x+33

Back to the equation:

-(6x+33)


We get rid of parentheses

36x^2-54x-6x-33=0

We add all the numbers together, and all the variables

36x^2-60x-33=0

a = 36; b = -60; c = -33;
Δ = b2-4ac
Δ = -602-4·36·(-33)
Δ = 8352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8352}=\sqrt{144*58}=\sqrt{144}*\sqrt{58}=12\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{58}}{2*36}=\frac{60-12\sqrt{58}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{58}}{2*36}=\frac{60+12\sqrt{58}}{72}
$